Check right after crossing (4-4)
I believe the answer is:
once-over
'check right' is the definition.
'once-over' can be an answer for 'check' (I have seen 'Brief check' mean 'once-over' so perhaps 'check' could also mean 'once-over'). I'm not certain of the 'right' bit.
'after crossing' is the wordplay.
'after' becomes 'once' (once can mean immediately after).
'crossing' becomes 'over' (I can't justify this - if you can you should believe this answer much more).
'once'+'over'='ONCE-OVER'
Can you help me to learn more?
(Other definitions for once-over that I've seen before include "Quick appraisal" , "Brief check" , "Quick inspection" , "Appraising glance" , "Cursory examination" .)